Superparamagnetism in the Low-Temperature Limit of Ising Models

It is shown that at low magnetic fields the low-temperature limit of a linear antiferromagnetic system containing a small concentration of frozen-in ferromagnetically coupled impurities is an analog to a random walk with restricted reversals. This results in the equivalence of the average chain to a single free spin of magnitude q½/2, where q is the number of impurities in the chain. The high field magnetization probably increases in steps of increasing height and width in the region in which the magnetic field overcomes the impurity exchange coupling. Possible generalizations to more dimensions and intermediate coupling are discussed. The frozen-in impurities and a gas of impurities may serve, respectively, as lower and upper bounds on a broader class of problems. An experiment for measuring the correlations 〈σ1, σn〉 between distant spins is suggested. The lack of field saturation and large decrease in susceptibility of certain organic free radicals is discussed.